A packet contained purple, black and red staplers. ²₅ of the staplers were purple and ⁴₉ of the remainder were black staplers.The rest were red staplers.

1. Find the ratio of the number of red staplers to the number of purple staplers.
2. There were 176 fewer black staplers than purple staplers. How many staplers were there in the packet?

Purple staplers	Black staplers	Red staplers
2x3	3x3
	4x1	5x1
6 u	4 u	5 u

(a)
Fraction of purple staplers = ²₅
Fraction of staplers that are not purple = 1 - ²₅ = ³₅

Remaining fraction of black staplers = ⁴₉
Remaining fraction of red staplers = 1 - ⁴₉ = ⁵₉

The total number of black staplers and red staplers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 3 and 9 = 9

Red staplers : Purple staplers
5 : 6

(b)
Difference in the number of purple staplers and black staplers
= 6 u - 4 u
= 2 u

2 u = 176
1 u = 176 ÷ 2 = 88

Total number of staplers
= 6 u + 4 u + 5 u
= 15 u
= 15 x 88
= 1320

Answer(s): (a) 5 : 6; (b) 1320